What is the derivative of 5x^4-3x^2+1/(sqrt(x)-7) ?

The derivative of 5x^4-3x^2+1/(sqrt(x)-7) is (40x^{9/2}-12x^{5/2}-1)/(2xsqrt(x))

What is the first derivative of 5x^4-3x^2+1/(sqrt(x)-7) ?

The first derivative of 5x^4-3x^2+1/(sqrt(x)-7) is (40x^{9/2}-12x^{5/2}-1)/(2xsqrt(x))

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\frac{d}{d x} (5 x^{4} - 3 x^{2} + \frac{1}{x} - 7)

\frac{40 x ^{\frac{9}{2}} - 12 x ^{\frac{5}{2}} - 1}{2 x x}

Solution steps

\frac{d}{d x} (5 x^{4} - 3 x^{2} + \frac{1}{x} - 7)

Simplify

5 x^{4} - 3 x^{2} + \frac{1}{x} - 7 : \frac{1 + 5 x ^{\frac{9}{2}} - 3 x ^{\frac{5}{2}}}{x} - 7

= \frac{d}{d x} (\frac{1 + 5 x ^{\frac{9}{2}} - 3 x ^{\frac{5}{2}}}{x} - 7)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1 + 5 x ^{\frac{9}{2}} - 3 x ^{\frac{5}{2}}}{x}) - \frac{d}{d x} (7)

\frac{d}{d x} (\frac{1 + 5 x ^{\frac{9}{2}} - 3 x ^{\frac{5}{2}}}{x}) = \frac{40 x ^{\frac{9}{2}} - 12 x ^{\frac{5}{2}} - 1}{2 x x}

\frac{d}{d x} (7) = 0

= \frac{40 x ^{\frac{9}{2}} - 12 x ^{\frac{5}{2}} - 1}{2 x x} - 0

Simplify

= \frac{40 x ^{\frac{9}{2}} - 12 x ^{\frac{5}{2}} - 1}{2 x x}

\int \frac{1}{3 + 3 cos ( x )} d x

\frac{\partial}{\partial x} (ln (x cos (y)))

\int 3 t^{2} sin (t^{3}) d t

\frac{d}{d x} ((x)^{3})

What is the derivative of 5x^4-3x^2+1/(sqrt(x)-7) ?
The derivative of 5x^4-3x^2+1/(sqrt(x)-7) is (40x^{9/2}-12x^{5/2}-1)/(2xsqrt(x))
What is the first derivative of 5x^4-3x^2+1/(sqrt(x)-7) ?
The first derivative of 5x^4-3x^2+1/(sqrt(x)-7) is (40x^{9/2}-12x^{5/2}-1)/(2xsqrt(x))